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A value iteration algorithm for time-aggregated Markov-decision processes (MDPs) is developed to solve problems with large state spaces. The algorithm is based on a novel approach which solves a time aggregated MDP by incrementally solving a set of standard MDPs. Therefore, the algorithm converges under the same assumption as standard value iteration. Such assumption is much weaker than that required by the existing time aggregated value iteration algorithm. The algorithms developed in this paper are also applicable to MDPs with fractional costs.